Solution: A parallel line passing through point A is BC, which intersects the extension line of BF at point M.

Because f is the midpoint of AC, so △AMF=△CBF, so AM=BC, MF=BF.

Let AM=BC=3a,

Because D and E divide BC into three parts, BD = DE = EC = A.

Because AM is parallel to BC, △AMQ is similar to △EBQ, and △AMP is similar to △DBQ.

So MP/BP = AM/DB = 3A/A = 3Mq/BQ = AM/EB = 3A/2A = 3/2.

Let BP=X, PQ=Y, QF = Z.

MP/BP =(X+Y+Z+Y+Z)/X = 3mq/BQ =(X+Y+Z+Z)/(X+Y)= 3/2

Simplified to X=Y+Z 4Z=X+Y

So x: y: z = 5: 3: 2.

So BP: PQ: QF = 5: 3: 2.